Is Skipping Calculus I and Going Straight to Calc II a Good Idea?

In summary, the conversation discusses a high school student who is currently in precalculus and planning to skip Calculus I over the summer. The student's school will test them with the AB Calculus AP exam and they plan on taking Calculus I through Columbia University's Summer Session. The main concern is whether this will provide enough preparation for Calculus II next year. The conversation also includes descriptions of Calculus I and II courses from the high school and Columbia University, as well as suggestions for the student's future math studies. Some concerns are raised about the validity of the AP test and the cost of college credit.
  • #1
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Hello,
I am a freshman in High School currently, I am in precalculus. I am intending to skip Calculus I over the summer. I know my school will test me with the AB Calculus APexam and I was planning on taking Calculus I through Columbia University's Summer Session. Will this be enough preparation, and will I be able to do well in Calculus II next year?

Here is my High Schools Course Descriptions of Calc I and II

"Description: AP Calculus I/AB is a rigorous college-level course which emphasizes a multirepresentational approach to calculus, with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally. Topics covered include the initial review of pre-calculus topics, limits, differentiation and its applications, and integration and its applications. There is an emphasis on problem solving, working collaboratively, and
communicating mathematically in both written and oral form. Graphing calculators are used in class on a daily basis and are provided by the school. Since this is an Advanced Placement college-level course, students are expected to spend a considerable amount of time outside of class in homework preparation and daily studying. An Advanced Placement exam will be given through the College Board in May."

"Description: Calculus II is a rigorous college level course that emphasizes a multirepresentational approach to calculus. Students learn to express mathematical concepts geometrically, numerically, analytically, and verbally. As a continuation of Calculus I, topics covered in this class include applications and techniques of integration, L’Hopitals’ Rule, improper integrals, an introduction to differential equations, infinite series and sequences, conic
sections, parametric and polar equations. Students who enroll in Calculus II will be expected to participate in a collaborative learning environment. As in Calculus I, problem solving and mathematical communication in written and oral form are an essential component of this course. Graphing calculators are utilized extensively and are provided by the school. Calculus II is an
Advanced Placement, college level course. Therefore, all students are expected to spend considerable time outside of class in homework preparation and daily study. An Advanced Placement exam will be given through the College Board in May."

Columbia's Description of Calculus I
"Course Description: Functions, limits, derivatives, introduction to integrals."
and a sample syllabus http://www.math.columbia.edu/department/syllabi/CalcIsyllabus.html


Thanks For your input! And if anyone has experience with Columbia's Summer Session, Private Message me por favor.
 
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  • #2
The only problem I see with taking calculus over the summer is that the AP test won't be until next spring, but if you continue with the calculus 2 class you may be able to take the AP Calculus BC test which covers more material than the AB test. Otherwise, if you can handle it, then go for it.
 
  • #3
The time-scale for studying a course should effectively be based on quantity of weeks - NOT quantity of hours. If the summer session Calculus 1 course is of fewer weeks than this course would be during the normal semester season, then you will not have enough weeks to study and learn effectively. Give yourself the full length of the summer to study the Calculus 1 course thoroughly. This means, give yourself more than or equal to 12 weeks to study (which should really be close to 18 weeks during a normal semester). Typically, summer sessions are not more than 6 weeks. Most people can not really study a course effectively in 6 weeks; too hard; not enough weeks to develop. (although some people are "smarter" or mentally "stronger" and may be able to do it.)
 
  • #4
also do you have any plans to study math after you finish calc 1 and two?

if you intend to continue studying math/physics/<insert technical subject involving calculus here> you shouldhave a plan as to where you can take courses beyond calc 1/2. Otherwise you may find yourself forgetting some ofhe material over your junior and senior year and then you may have trouble going into a college math class.
 
  • #5
Ok
d_Leet - My school will test me with one of the declassifyied AP exams from the past (AB 2003 form- A) (don't ask how i know that) so that's not a problem really

Symbolipoint - I feel that I could accomplish the learning in 6 weeks effectively, and i would still have another three weeks after the summer course to study on my own.

CPL. Luke- My high school offers Multivariable calculus after calc 2 and i can take math my senior year at a local college, or i can just chillax and take prob and stat, but I really intend on taking Linear Algebra after Calc 3, if that makes sense?
 
  • #6
that works then, as long as you aren't doing nothing in those years you won't have a problem
 
  • #7
dtl42 said:
Ok
d_Leet - My school will test me with one of the declassifyied AP exams from the past (AB 2003 form- A) (don't ask how i know that) so that's not a problem really

Ok that's fine my point is that that test won't count for college credit though because I really doubt than any college will accept an AP score from an unofficial test that was given several years ago and which by now certainly has answers easily accesible.
 
  • #8
But if he takes the course at Columbia, most any place he goes for college will probably accept it as transfer credit for their Calc I.
 
  • #9
I always wondered why high school students didn't just take calculus from the community college. In two semesters they cover vastly more than the one year in high school covers, and the treatment is likely more rigorous. Also, no stress over AP exams, just take credit to your next university with you.
 
  • #10
colin.mcenroe said:
I always wondered why high school students didn't just take calculus from the community college. In two semesters they cover vastly more than the one year in high school covers, and the treatment is likely more rigorous. Also, no stress over AP exams, just take credit to your next university with you.

AP exam=$80
college credit=$600 min
 
  • #11
Wow, what community college charges that much? That is over the top! The school I went to charged $28 per unit, which is rather high. A five unit math course would run close to $150 and with some other fees maybe a bit more. The books are not cheap, but you can hunt and find one used for $20 usually. But the thing about my high school (and I never used this opportunity) is that enrollment was at something like $1 or $3 per unit if I remember correctly. $600 is probably the most I ever shelled out for a semester at a community college with books, 19 units, and everything else. Tuition used to be free!

But regardless, the experience you will have in a college classroom vs. a high school AP course with high school students is much more valuable. You will leave the class with a calculus text that you can use in the future (which I frequently do, in fact I have three of them). You will also see how a college class functions vs. a high school class. You will experience the lack of "messing around" that is acceptable in high school. You will call your teachers "Professor" instead of "Mrs./Mr." You will just get a flavor for the less personal nature you will experience after you go on.

At my high school the highest anyone would have possibly been able to test was the Calculus AB exam, and that was after nearly an entire year of school. If you want to get ahead of everyone, go to the community college.

I do understand why someone might want to stay on campus just for social reasons, I just remember being jealous of all the students who didn't take AP exams because they were smart enough to take the courses at a college. I think seeing actual college experience is a plus for those who are trying to be competitive in their applications to big universities, too. It just shows the ability to do well in a college environment, sort of like applying to your first job w/o any experience vs. a couple of years under your belt. Of course, if it is your senior year there are a lot of feelings of "the last chance" and sentimentality over friendships and your school, so I understand not wanting to spend all of your time off campus at a cold community college. Anyway, have a good year and enjoy yourself.

Colin
 
  • #12
colin.mcenroe said:
Wow, what community college charges that much? That is over the top! The school I went to charged $28 per unit, which is rather high. A five unit math course would run close to $150 and with some other fees maybe a bit more. The books are not cheap, but you can hunt and find one used for $20 usually. But the thing about my high school (and I never used this opportunity) is that enrollment was at something like $1 or $3 per unit if I remember correctly. $600 is probably the most I ever shelled out for a semester at a community college with books, 19 units, and everything else. Tuition used to be free!
Just to see what some of the fees look like, here's a sampling from across the country:
http://www.mccc.edu/admissions_tuition.shtml
http://www.oakton.edu/admiss/tuition.htm
http://www.scottsdalecc.edu/admissions/tuition/2006-2007_tuition.html [Broken]

I would think it would also depend on whether a summer course at a community college will satisfy your high school's requirements for graduation. All the advanced coursework in the world isn't going to help you out in college if you don't get your high school diploma first.

I think it's also important to consider the pace at which the courses are taught. Someone may be getting excellent grades in high school courses because they are taught at a slower pace, but college level courses in the summer are condensed into such a short period of time that even college students can struggle to keep up with that pace. If you take a course during the regular academic year, you may have two or three weeks to read, study, digest and learn the material that is covered in only one week in a summer course. In a high school, that amount of material might be covered over a month.
 
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  • #13
Ok for all you guys, I am actually going to Columbia University for this summer and not a community college, the community college was only an option for after junior year (multivariable).
 
  • #14
Congratulations with Columbia, be careful, it is in a bad neighborhood! Seems like we moved into a discussion on community college here.

Pretty surprising how expensinve these community colleges are! I guess here in CA we have it pretty good. Everyone made a huge fuss when Arnold raised the tuition by about $10. At any rate, our $28 a unit used to be $11 a unit, and it has continually gone up. Still, it doesn't compare to the ~$2500 education fee we are paying every quarter at UC!
 
  • #15
Hey, original poster, just noticed that you are a freshman in high school! Wow, you are very advanced in math for a freshman. If I had known that I would have said to just stick with your high school classes until you run out of them since you have so much time.
 
  • #16
o thanks a lot, i really feel the need to set myself apart from the other millions of students applying to top colleges and this is surely one method to go about that i believe.
 
  • #17
An AP calculus test covers very little. Any full course would be much more valuable. At your age, saving time is a ludicrous reason to bypass a thorough treatment of the material.

The price of a full course is worth it if your goal is to learn calculus. No one can learn calculus well in a few weeks. Even at Columbia, the purpose of the summer school is likely to make money for the university, not to provide a thorough training for the students.

Look who the instructors are, I'll wager they are not regular Columbia professors.

Maybe if you work at it all day every day, you might be ok if you get an A.
 
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  • #18
Alright now that I've decided that i am skipping and that columbia's program is sufficient, i need some input on my grades.

Through half a year i have
Bio - 93
Eng- 94
World History - 93
Spanish - 95
Fitness - 100
Health - 97
Algebra - 100 (first half only)
Math analysis( precalc) - 100
Graphics and Design - 93
Foundations of Science/ Scientific Data Analysis - 95Do you think these grades will be sufficient to be accepted into Columbia's summer program, the only class I am taking will be Calculus I
 
  • #19
Mathwonk- Well the Calculus II class at my school thoroughly reviews ( first three eigths of the year) Calculus I, and I have plenty of time senior year to do anything, even if that means reviewing calculus I and II.
 
  • #20
I just looked at the website for the Columbis courses, and not a single one of the 5-6 sections is taught by a member of the Columibia math faculty, as you can check by looking at their website.Just don't kid yourself, that summer course is NOT equivalent to a regular Columbia university calculus course. If you are being charged a high price, in all likelihood it is for their name, not for their professors.
 
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  • #21
But that's irrelevant isn't it? Calculus is calculus right? so the teacher doesn't matter all that much, as long as its not some fluff-head I think id be alright, and any input on how my grades look, and if its that hard to get in?
 
  • #22
I just looked at the website for the Columbis courses, and not a single one of the 5-6 sections is taught by a member of the Columibia math faculty, as you can check by looking at their website.Just don't kid yourself, that summer course is NOT equivalent to a regular Columbia university calculus course. If you are being charged a high price, in all likelihood it is for their name, not for their professors.

I guarantee you it will not be hard to get in, it is a money making venture, not an academic competition.
 
  • #23
Well money isn't an issue, but prestige is, my father is a rather biased man, who came to the USA at age 15 not knowing english, and worked his way to cornell, then rutgers for law school, then chicago medical school, then columbia, and then penn, so he wants me to go to ivy's all the way for the most part, and i frankly don't feel like arguing with him.
 
  • #24
i just searched for you on the websites of harvard, columbia, chicago, brown, and none of them offer a summer calculus course taught by a member of their own faculty. so people like your father who mean well, but pay for name recognition, are being sold a bill of goods.

It is conceivable that a school like UGA where I teach, may offer a summer course actually taught by a faculty member, but i cannot find a listing for us. I myself will not teach one because I want to vacation with my wife and do research in my summer.

Of course even if i did teach I could not convince some people to take it.

I recommend instead you consider taking the PROMYS course at Boston University, where you will actually be challenged to do some research and learn some advanced topics in number theory.

here is the website.

http://www.promys.org/

The other students will be other bright high schoolers, and the program is run by people who are researchers and teachers in number theory like Glenn Stevens.

Bright high schoolers should take courses designed for them, rather than courses designed for dull college students, which is what summer courses in uni often are.
 
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  • #25
I don't necessarily want to do research, id rather skip calculus, it may seem illogical, but i just want to do it. And my father is not actually in theory paying for the calculus ( that's what i would prefer) but he is in fact paying for the name, he could probably care less about whether i skip calculus or not, but I have to do it at a University of his approval pretty much. So its his intention to merely pay for the name, and i am stil learning so i have no major complaint.
 
  • #26
well it is true that even a mediocre summer uni calc course is in all likelihood better than a high chool course, so it should be ok.

what is your goal, since you say you are not wanting to do research?
 
  • #27
You know I am not really sure, that's something i could really use some help on. I love math, but i would love to get into politics (not really viable) so i was thinking something in math or in science, something that would put me on a path to be doing research eventually, but not now. I feel i need to make certain of my ability to compute the basics needed for really advanced stuff. Any suggestions of things to do? anything at all, you said you teach, what to you teach?
 
  • #28
I am a profesional algebraic geometer, and a father myself, and when my first son showed talent in math, I wanted to push him in that direction, and have him go to harvard, and have the career that I wanted to have myself, but did not. I thought with my guidance he could be the math whiz I was not.

He applied to Harvard to please me, and got in, but at a certain point told
me he loved me, but he wanted to make his own choices and live his own life. He turned down Harvard, much to my dismay, went to Stanford, and is a very happy man, living on the west coast.

Best wishes to you and your dad as you sort this out yourselves. I am sure you also love each other and want to please each other, and you will manage it somehow.

if you want to know about the subject I teach and love, see my thread, who wants to be amathematician?
 
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1. Is Skipping Calculus I a common practice?

No, it is not a common practice. Most students take Calculus I before moving on to Calculus II.

2. What are the potential consequences of skipping Calculus I?

The potential consequences include missing important foundational concepts and struggling in Calculus II. It may also lead to difficulty in higher-level math courses.

3. Can skipping Calculus I save time?

Skipping Calculus I may save time in the short term, but it can lead to longer-term consequences such as struggling in future math courses. It is important to have a strong foundation in Calculus I before moving on to Calculus II.

4. Is it possible to catch up on the material from Calculus I while taking Calc II?

It is possible to catch up on the material, but it may require extra effort and time outside of class. This may be challenging, especially if the student is also taking other courses and has a busy schedule.

5. Are there any exceptions where skipping Calculus I may be a good idea?

In some cases, students who have a strong background in pre-calculus and have demonstrated proficiency in calculus concepts through advanced placement (AP) or International Baccalaureate (IB) exams may be able to skip Calculus I. However, it is still recommended to consult with a math advisor before making this decision.

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